So clearly you can't use the triangular prism formula for this question , but you an generalize it looking what it describes.

I don't know what they gave you, but the surface area of a triangular prism consists of
2 congruent triangular bases + 3 congruent rectangles

so the surface area of a pentagon
= 2 (area of the pentagon) + 5rectangles

you are given that the perimeter is 20, so each side of the base is 20/5 = 4, and the height is 10
so the surface area of the 5 rectangles is 5(4)(10) = 200
add the 2 pentagon areas of 32 each for a total of

200 + 64 = 264 cm^2

your text should give you the definitions of lateral and total surface areas, make the necessary adjustments.